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src/cpu/x86/vm/sharedRuntime_x86_64.cpp

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*** 21,30 **** --- 21,33 ---- * questions. * */ #include "precompiled.hpp" + #ifndef _WINDOWS + #include "alloca.h" + #endif #include "asm/macroAssembler.hpp" #include "asm/macroAssembler.inline.hpp" #include "code/debugInfoRec.hpp" #include "code/icBuffer.hpp" #include "code/vtableStubs.hpp"
*** 3964,3973 **** --- 3967,4220 ---- // frame_size_words or bytes?? return RuntimeStub::new_runtime_stub(name, &buffer, frame_complete, frame_size_in_words, oop_maps, true); } + //------------------------------Montgomery multiplication------------------------ + // + + #ifndef _WINDOWS + + #define ASM_SUBTRACT + + #ifdef ASM_SUBTRACT + // Subtract 0:b from carry:a. Return carry. + static unsigned long + sub(unsigned long a[], unsigned long b[], unsigned long carry, long len) { + long i = 0, cnt = len; + unsigned long tmp; + asm volatile("clc; " + "0: ; " + "mov (%[b], %[i], 8), %[tmp]; " + "sbb %[tmp], (%[a], %[i], 8); " + "inc %[i]; dec %[cnt]; " + "jne 0b; " + "mov %[carry], %[tmp]; sbb $0, %[tmp]; " + : [i]"+r"(i), [cnt]"+r"(cnt), [tmp]"=&r"(tmp) + : [a]"r"(a), [b]"r"(b), [carry]"r"(carry) + : "memory"); + return tmp; + } + #else // ASM_SUBTRACT + typedef int __attribute__((mode(TI))) int128; + + // Subtract 0:b from carry:a. Return carry. + static unsigned long + sub(unsigned long a[], unsigned long b[], unsigned long carry, int len) { + int128 tmp = 0; + int i; + for (i = 0; i < len; i++) { + tmp += a[i]; + tmp -= b[i]; + a[i] = tmp; + tmp >>= 64; + assert(-1 <= tmp && tmp <= 0, "invariant"); + } + return tmp + carry; + } + #endif // ! ASM_SUBTRACT + + // Multiply (unsigned) Long A by Long B, accumulating the double- + // length result into the accumulator formed of T0, T1, and T2. + #define MACC(A, B, T0, T1, T2) \ + do { \ + unsigned long hi, lo; \ + asm("mul %5; add %%rax, %2; adc %%rdx, %3; adc $0, %4" \ + : "=&d"(hi), "=a"(lo), "+r"(T0), "+r"(T1), "+g"(T2) \ + : "r"(A), "a"(B) : "cc"); \ + } while(0) + + // As above, but add twice the double-length result into the + // accumulator. + #define MACC2(A, B, T0, T1, T2) \ + do { \ + unsigned long hi, lo; \ + asm("mul %5; add %%rax, %2; adc %%rdx, %3; adc $0, %4; " \ + "add %%rax, %2; adc %%rdx, %3; adc $0, %4" \ + : "=&d"(hi), "=a"(lo), "+r"(T0), "+r"(T1), "+g"(T2) \ + : "r"(A), "a"(B) : "cc"); \ + } while(0) + + // Fast Montgomery multiplication. The derivation of the algorithm is + // in A Cryptographic Library for the Motorola DSP56000, + // Dusse and Kaliski, Proc. EUROCRYPT 90, pp. 230-237. + + static void __attribute__((noinline)) + montgomery_multiply(unsigned long a[], unsigned long b[], unsigned long n[], + unsigned long m[], unsigned long inv, int len) { + unsigned long t0 = 0, t1 = 0, t2 = 0; // Triple-precision accumulator + int i; + + assert(inv * n[0] == -1UL, "broken inverse in Montgomery multiply"); + + for (i = 0; i < len; i++) { + int j; + for (j = 0; j < i; j++) { + MACC(a[j], b[i-j], t0, t1, t2); + MACC(m[j], n[i-j], t0, t1, t2); + } + MACC(a[i], b[0], t0, t1, t2); + m[i] = t0 * inv; + MACC(m[i], n[0], t0, t1, t2); + + assert(t0 == 0, "broken Montgomery multiply"); + + t0 = t1; t1 = t2; t2 = 0; + } + + for (i = len; i < 2*len; i++) { + int j; + for (j = i-len+1; j < len; j++) { + MACC(a[j], b[i-j], t0, t1, t2); + MACC(m[j], n[i-j], t0, t1, t2); + } + m[i-len] = t0; + t0 = t1; t1 = t2; t2 = 0; + } + + while (t0) + t0 = sub(m, n, t0, len); + } + + // Fast Montgomery squaring. This uses asymptotically 25% fewer + // multiplies so it should be up to 25% faster than Montgomery + // multiplication. However, its loop control is more complex and it + // may actually run slower on some machines. + + static void __attribute__((noinline)) + montgomery_square(unsigned long a[], unsigned long n[], + unsigned long m[], unsigned long inv, int len) { + unsigned long t0 = 0, t1 = 0, t2 = 0; // Triple-precision accumulator + int i; + + assert(inv * n[0] == -1UL, "broken inverse in Montgomery multiply"); + + for (i = 0; i < len; i++) { + int j; + int end = (i+1)/2; + for (j = 0; j < end; j++) { + MACC2(a[j], a[i-j], t0, t1, t2); + MACC(m[j], n[i-j], t0, t1, t2); + } + if ((i & 1) == 0) { + MACC(a[j], a[j], t0, t1, t2); + } + for (; j < i; j++) { + MACC(m[j], n[i-j], t0, t1, t2); + } + m[i] = t0 * inv; + MACC(m[i], n[0], t0, t1, t2); + + assert(t0 == 0, "broken Montgomery square"); + + t0 = t1; t1 = t2; t2 = 0; + } + + for (i = len; i < 2*len; i++) { + int start = i-len+1; + int end = start + (len - start)/2; + int j; + for (j = start; j < end; j++) { + MACC2(a[j], a[i-j], t0, t1, t2); + MACC(m[j], n[i-j], t0, t1, t2); + } + if ((i & 1) == 0) { + MACC(a[j], a[j], t0, t1, t2); + } + for (; j < len; j++) { + MACC(m[j], n[i-j], t0, t1, t2); + } + m[i-len] = t0; + t0 = t1; t1 = t2; t2 = 0; + } + + while (t0) + t0 = sub(m, n, t0, len); + } + + // Swap words in a longword. + static unsigned long swap(unsigned long x) { + return (x << 32) | (x >> 32); + } + + // Copy len longwords from s to d, word-swapping as we go. The + // destination array is reversed. + static void reverse_words(unsigned long *s, unsigned long *d, int len) { + d += len; + while(len-- > 0) { + d--; + *d = swap(*s); + s++; + } + } + + // The threshold at which squaring is advantageous was determined + // experimentally on an i7-3930K (Ivy Bridge) CPU @ 3.5GHz. + #define MONTGOMERY_SQUARING_THRESHOLD 64 + + void SharedRuntime::montgomery_multiply(jint *a_ints, jint *b_ints, jint *n_ints, + jint len, jlong inv, + jint *m_ints) { + assert(len % 2 == 0, "array length in montgomery_multiply must be even"); + int longwords = len/2; + + // Make very sure we don't use so much space that the stack might + // overflow. 512 jints corresponds to an 16384-bit integer and + // will use here a total of 8k bytes of stack space. + int total_allocation = longwords * sizeof (unsigned long) * 4; + guarantee(total_allocation <= 8192, "must be"); + unsigned long *scratch = (unsigned long *)alloca(total_allocation); + + // Local scratch arrays + unsigned long + *a = scratch + 0 * longwords, + *b = scratch + 1 * longwords, + *n = scratch + 2 * longwords, + *m = scratch + 3 * longwords; + + reverse_words((unsigned long *)a_ints, a, longwords); + reverse_words((unsigned long *)b_ints, b, longwords); + reverse_words((unsigned long *)n_ints, n, longwords); + + ::montgomery_multiply(a, b, n, m, (unsigned long)inv, longwords); + + reverse_words(m, (unsigned long *)m_ints, longwords); + } + + void SharedRuntime::montgomery_square(jint *a_ints, jint *n_ints, + jint len, jlong inv, + jint *m_ints) { + assert(len % 2 == 0, "array length in montgomery_square must be even"); + int longwords = len/2; + + // Make very sure we don't use so much space that the stack might + // overflow. 512 jints corresponds to an 16384-bit integer and + // will use here a total of 6k bytes of stack space. + int total_allocation = longwords * sizeof (unsigned long) * 3; + guarantee(total_allocation <= 8192, "must be"); + unsigned long *scratch = (unsigned long *)alloca(total_allocation); + + // Local scratch arrays + unsigned long + *a = scratch + 0 * longwords, + *n = scratch + 1 * longwords, + *m = scratch + 2 * longwords; + + reverse_words((unsigned long *)a_ints, a, longwords); + reverse_words((unsigned long *)n_ints, n, longwords); + + if (len >= MONTGOMERY_SQUARING_THRESHOLD) { + ::montgomery_square(a, n, m, (unsigned long)inv, longwords); + } else { + ::montgomery_multiply(a, a, n, m, (unsigned long)inv, longwords); + } + + reverse_words(m, (unsigned long *)m_ints, longwords); + } + + #endif // WINDOWS + #ifdef COMPILER2 // This is here instead of runtime_x86_64.cpp because it uses SimpleRuntimeFrame // //------------------------------generate_exception_blob--------------------------- // creates exception blob at the end
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